Gas turbine engines can include fluid damped bearings to help maintain vibration and displacement of rotating components within acceptable limits. Typically, these fluid damped bearings are fed oil from the engine oil system and accept the oil at a pressure generated by the system. Typical systems regulate fluid flow to the fluid damped bearing with a valve that switches between on and off positions. In some cases, however, alternating between on and off positions exclusively can cause the oil flow rate to stray from an optimal flow rate to a rate that is either too high or too low. Either condition can lead to undesired vibration and displacement of rotating components during operation of the gas turbine engine. There is, accordingly, a need for a fluid damped bearing system that can help maintain an optimum flow of fluid to the fluid damped bearing during operation of the gas turbine engine.